Fragmentation reactions in a carbon target with beams of Li-11 and Be-14 at relativistic energies have been studied in a kinematically complete experiment at the ALADIN-LAND setup at GSI. Excited states in Li-11 and Be-14 were obtained from the data in the inelastic channel. The measured cross sections with the core nucleus in the final state show that in the Be-14 case core polarization plays an important role. In the one-neutron knockout channels the measured angular correlations between fragment and neutron are asymmetric, which demonstrates the presence of states with different parities in the Li-11 and Be-14 ground states. For Li-10 a low-lying virtual s-state, a p-state and evidence for a d-state could be extracted from the data, while the Be-12 + n system shows resonances with more complicated structure.